trigonometrical table

简明释义

三角函数表

英英释义

例句

1.When calculating distances in navigation, sailors use a trigonometrical table to determine angles.

在导航中计算距离时，水手使用三角函数表来确定角度。

2.In geometry class, we often refer to the trigonometrical table to find the values of sine and cosine.

在几何课上，我们经常参考三角函数表来查找正弦和余弦的值。

3.The trigonometrical table is essential for anyone studying physics or engineering.

对于任何学习物理或工程的人来说，三角函数表都是必不可少的。

4.During the exam, I forgot to bring my trigonometrical table, which made it difficult to solve the problems.

在考试期间，我忘记带我的三角函数表，这让我很难解决问题。

5.To solve this triangle, we need to consult the trigonometrical table for the angles.

要解决这个三角形，我们需要查阅三角函数表来获取角度。

作文

In the realm of mathematics, particularly in trigonometry, the concept of a trigonometrical table plays an essential role. A trigonometrical table is a systematic arrangement of the values of trigonometric functions for various angles, typically ranging from 0 to 90 degrees. These tables are vital for students and professionals who need to calculate sine, cosine, tangent, and their respective inverses without the aid of calculators or computers. Understanding how to read and utilize a trigonometrical table can significantly enhance one's ability to solve problems related to triangles and periodic functions.Historically, trigonometrical tables were created long before the advent of modern technology. Ancient mathematicians recognized the need for quick reference tools to facilitate calculations in astronomy, navigation, and architecture. The earliest known trigonometrical tables date back to the Babylonians and Greeks, who developed methods to approximate the values of these functions. As mathematics evolved, so did the precision and scope of these tables.A typical trigonometrical table includes values for sine (sin), cosine (cos), and tangent (tan) for angles expressed in degrees or radians. For example, the sine of 30 degrees is 0.5, while the cosine of 60 degrees is also 0.5. These relationships are fundamental in solving various geometric problems, such as finding the height of a tree using the angle of elevation and the distance from the tree.Moreover, the significance of trigonometrical tables extends beyond pure mathematics; they are also crucial in fields such as physics and engineering. For instance, when analyzing wave patterns or oscillations, engineers often rely on these tables to determine the appropriate angles and forces involved. In essence, mastering the use of a trigonometrical table equips individuals with the tools necessary to tackle complex real-world problems.In today's digital age, one might wonder if trigonometrical tables are still relevant. While calculators and computer software have largely replaced the need for manual calculations, understanding the underlying principles of trigonometry and being able to interpret a trigonometrical table remains crucial. It fosters a deeper comprehension of mathematical concepts and enhances problem-solving skills. Furthermore, in examinations or situations where electronic devices are prohibited, proficiency in using a trigonometrical table can be invaluable.To effectively use a trigonometrical table, one must first familiarize themselves with the layout of the table. Typically, the angles are listed in one column, while the corresponding values of sine, cosine, and tangent are presented in adjacent columns. By locating the desired angle, one can quickly find the necessary trigonometric values. Practice is key; the more one engages with a trigonometrical table, the more adept they will become at interpreting and applying its information.In conclusion, the trigonometrical table is a fundamental tool in the study of trigonometry. Its historical significance, practical applications, and continued relevance in education and various professions underscore the importance of mastering this resource. Whether you are a student grappling with trigonometric concepts or a professional applying these principles in your work, understanding how to effectively utilize a trigonometrical table is essential for success in the field of mathematics and beyond.

在数学领域，尤其是在三角学中，trigonometrical table（三角函数表）的概念扮演着重要角色。trigonometrical table 是一个系统地排列各种角度的三角函数值的表格，通常范围从0到90度。这些表格对于需要计算正弦、余弦、正切及其反函数的学生和专业人士至关重要，尤其是在没有计算器或电脑的情况下。理解如何阅读和利用trigonometrical table 可以显著提升解决与三角形和周期函数相关问题的能力。历史上，trigonometrical tables 在现代科技出现之前就已经被创建。古代数学家意识到快速参考工具的需求，以便于在天文学、航海和建筑等领域进行计算。已知最早的trigonometrical tables可以追溯到巴比伦人和希腊人，他们开发了近似这些函数值的方法。随着数学的发展，这些表格的精确性和范围也不断扩大。一个典型的trigonometrical table 包括正弦（sin）、余弦（cos）和正切（tan）在以度数或弧度表示的角度下的值。例如，30度的正弦是0.5，而60度的余弦也是0.5。这些关系在解决各种几何问题时是基础，例如使用仰角和距离来求树木的高度。此外，trigonometrical tables 的重要性超越了纯数学；它们在物理和工程等领域也至关重要。例如，在分析波动模式或振荡时，工程师常常依赖这些表格来确定相关的角度和力。因此，掌握使用trigonometrical table 的技能使个人具备了解决复杂现实问题的能力。在今天的数字时代，人们可能会想知道trigonometrical tables 是否仍然相关。虽然计算器和计算机软件在很大程度上取代了手动计算的需求，但理解三角学的基本原理以及能够解读trigonometrical table 仍然至关重要。这有助于加深对数学概念的理解，并增强解决问题的能力。此外，在考试或禁止使用电子设备的情况下，熟练使用trigonometrical table 将是无价的。要有效使用trigonometrical table，首先必须熟悉表格的布局。通常，角度在一列中列出，而相应的正弦、余弦和正切值则呈现在相邻的列中。通过找到所需的角度，可以迅速找到必要的三角函数值。实践是关键；与trigonometrical table 的互动越多，解读和应用其信息的能力就越强。总之，trigonometrical table 是三角学研究中的基本工具。它的历史意义、实际应用以及在教育和各个职业中的持续相关性强调了掌握这一资源的重要性。无论你是正在努力理解三角学概念的学生，还是在工作中应用这些原理的专业人士，理解如何有效利用trigonometrical table 对于在数学及其相关领域取得成功至关重要。